Colored tensor models have recently burst onto the scene as a promising conceptual and
computational tool in the investigation of problems of random geometry in dimension three …

Written by the creator of the modern theory of random tensors, this book is the first self-
contained introductory text to this rapidly developing theory. Starting from notions familiar to …

Tensor models generalize random matrix models in yielding a theory of dynamical
triangulations in arbitrary dimensions. Colored tensor models have been shown to admit a …

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs
are dual to higher dimensional topological spaces. The perturbative development of the …

In this paper we generalize the results of Gurau (arXiv: 1011. 2726 [gr-qc], 2011), Gurau and
Rivasseau (arXiv: 1101.4182 [gr-qc], 2011) and derive the full 1/N expansion of colored …

In this paper, we perform the 1/N expansion of the colored three-dimensional Boulatov
tensor model. As in matrix models, we obtain a systematic topological expansion, with …

We prove that an integrated version of the Gurau colored tensor model supplemented with
the usual Bosonic propagator on U (1) 4 is renormalizable to all orders in perturbation …

The simplest non-commutative renormalizable field theory, the ϕ4 model on four-
dimensional Moyal space with harmonic potential is asymptotically safe up to three loops, as …

We study quartic matrix models with partition function ZE, J= ∫ dM ZE, J=∫ d M exp (trace
(JM-EM^ 2-λ 4 M^ 4)(JM-EM 2-λ 4 M 4)). The integral is over the space of Hermitean N …

This article is preface to the SIGMA special issue''Tensor Models, Formalism and
Applications'', http://www. emis. de/journals/SIGMA/Tensor_Models. html. The issue is a …